We Never See Nothing

I set up a BTC wallet through BitPay on my phone and I was given the twelve-word phrase to generate the private key in case I need to restore it as a backup.

I switched to the Coinbase wallet after that, and it asked me if I wanted to restore a wallet I already had by entering in the twelve-word backup phrase. So now I wonder: sometimes, I’m only given a BTC address on the Internet to pay for something, and my phone isn’t always available, so would it be safe (or feasible) to put this twelve-word phrase into another wallet program on my computer to access my BTC wallet? That way, I’d theoretically be able to access my money from both the computer and my phone.